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Transcript
Chapter 1 Notes Alg 1H 1-A2 (Lesson 1-3) “Open Sentences” p. 15-17 Open sentence: Solution: Equation: Inequality: Replacement set: Solution set: 1A) 1B) T/F T/F 1 2A) 2B) 3A) 3B) T/F T/F 4) 2 1-A8 (Lesson 1-7) “Logical Reasoning” Power Point Conditional statement: has a ________________ and a ________________ and is often written in ____________ form. Ex.: If the heat is too high, then the popcorn burns. 1) H: C: 2) H: C: *Note: Sometimes a conditional statement is triggered by the word “when” instead of “if”. Example: “We earn points when it is a COTY day.” Deductive reasoning: is a process that uses ___________, ___________, _____________________, and _______________________ to reach a valid conclusion. 3) 4) Counterexample: a ____________ case in which the _______________ is true and the _________________ is false. It takes only _________ counterexample to show that a conditional statement is ______________. 5) 6) 7) 3 The Real Number System Rational Numbers: numbers that can be written in the a form of . As a decimal they repeat or terminate. b 1 1 ex: 0.3333...... repeats ex: 0.25 terminates 3 4 Integers: Whole numbers and their opposites (this means positive and negative whole numbers). ex: …, ־4, ־3, ־2, ־1, 0, 1, 2, 3, 4, … Whole Numbers: Natural Numbers and zero. ex: 0,1,2,3… Natural or Counting: Numbers ex: 1,2,3,4,… So what isn’t a real number? divide by zero = undefined ( ), and numbers) are two examples. Irrational Numbers: ex: and 2 These must be represented by a symbol (ex: ), or as a rounded number, or in radical form because the decimal doesn’t repeat or terminate (stop). 1 = i (imaginary 4 1-A9 (Lesson 1-8) “Number Systems” p. 46-50 *calculator Read Ex. 1 1A) 6 11 1B) 9.16 Closure Property: determines if a solution to an operation is found in the ________________________ as are in the problem Read Ex. 2 2A) integers, division 2B) integers, addition Number line: o Has a ___________ under the line o Coordinate: the number that corresponds to a ___________ on a number line; labeled above the line o includes both _________________ and ___________________ numbers (values between the labeled values) Read Ex. 3 3A) {-5,-4,-3,-2,…} 3B) x 8 5 _________________: number that, when squared, results in the given value o Symbol is called a _____________ o Principal square root is ________________ o Only give the negative square root if there is a _______________ sign in front of the radical Read Ex. 4 4 121 4A) 4B) 1.69 Read Ex. 5 5) Compare real numbers: use a _________________ to approximate irrational square roots Read Ex. 6 6A) 2 2 ______ 3 5 6B) 0.8 _____ 8 9 Order real numbers: use decimal approximations Read Ex. 7 7A) 0.42, 0.63, 4 9 7B) 1.46, 0.2, 2, - 1 6 6 1-A10 (Lesson 1-9 “Functions and Graphs” p. 53-55 Function: a relationship between ________________ and _______________ Coordinate plane: formed by the intersection of two number lines o Horizontal axis: also called the ________________ and the ____________________ variable o Vertical axis: also called the ________________ and the ____________________ variable o Origin: the point where the two axes __________________; Ordered pair: labels a ___________ on a graph; has two ________________________, x and y (x, y) Read Ex. 1 1) Read Ex. 2 2A) I: D: 2B) I: D: Read Ex. 3 3) Relation: a set of ________________________ (x, y) Domain: set of values for the ______________________ variable; all the values of ____ Range: set of values for the ______________________ variable; all the values of ____ Discrete: _____________________ points Continuous: forms a _____________ or ______________ 7